There are two manufactures of coins: Manufacturer A and B. Both claim to make fair coins (p=0.5 where p is probability of heads), but they have only each verified this by flipping their coins 10 times and getting heads 5 times.

a) What model do you use to model the prior probability of p for both manufacturers?

b) You are given a coin from manufacturer A. You toss it 40 times yielding 23 heads.

Given this data, what is your new probability model for pmanufacturerA?

c) What is your expected value forpmanufacturerA given your answer for (b)?

d) You are given a coin from manufacturer B. You toss it 40 times yielding 30 heads. Given this data, what is your new probability model for pmanufacturerB?

e) What is your expected value forpmanufacturerB given your answer for (d)?

f) You are now given a third coin. And we want to determine who manufactured this coin. You toss the third coin 25 times and 16 are heads. Using your results from

(c) and (e) above, what are the probabilities that the coin was made by Manufacturer A or Manufacturer B?

g) Now imagine that you know that Manufacturer A made twice as many coins as Manufacturer B. How does this change you answers for (f)?